I fear it's the other way around. If you can find the performance characteristic of the EM-80, and the same for the mic you have in hand, then you may be able to analyze the circuit and make the changes that let it function with your mic.

There are several types of microphone available, and the label "EM-80" gives no clue as to the type it was. There is no low voltage out, so it may not have been an electret type - but I used to have some that had batteries to bias the element. It's almost certain that the EM-80 is not the same type as your "standard" type.

Of course the microphone is an electret type because it is biased.
The circuit will work with any two-wires electret mic.
The mic will not work if its polarity is connected backwards. The pin connected to its case is supposed to connect to ground and the other pin is its output.